by using 'unsubscribeEmail' you make it just string so use unsubscribeEmail instead of 'unsubscribeEmail'

function addURL(element) {
$(element).attr('href', function(){
    return this.href + 'unsubscribe-complete?q=direct_unsubscribe&fn=Public_DirectUnsubscribeForm&id=IDSTRING&' + unsubscribeEmail;
});
}